Can I create deep divots in my mesh using sculpt brush? Is there a better way without booleans?
Well, after banging away for a while I concluded that the brushes are not really made to creating deep pits like I was thinking, an that actually editing the mesh would make the realism I want. So I went back to an earlier version of the watch band, one with the subsurf modifier still intact, and added lots of loop cuts until most of my faces were squares and there were no long skinny triangles. Then I increased my subsurf level from 2 to 3, made a backup, and applied it. This gave me a ton of evenly distributed geometry to work with.

Then, rather than trying to do it with a brush, I simply went to the top-down view, in vertex select mode, used the circular selection tool, and just selected a blob of vertices near each entrance/exit point of the thread. 

Next I did proportional editing mode, sharp falloff, used individual origins, and just did G, Z to move the select vertices downward to create little pits. 

The result is what I had in mind and looks pretty good when rendered.